Suppression of Coulomb exchange energy in quasi-two-dimensional hole systems

TL;DR

This paper investigates how Coulomb exchange energy is suppressed in quasi-two-dimensional hole systems due to heavy-hole and light-hole mixing, providing analytical insights for spin-3/2 systems.

Contribution

It introduces a general formalism for calculating exchange energy in spinor-based many-particle systems and applies it to derive analytical results for hole systems.

Findings

Exchange energy is suppressed compared to conduction-band systems.

Strong heavy-hole and light-hole mixing reduces exchange energy.

Analytical results obtained for spin-3/2 hole systems.

Abstract

We have calculated the exchange-energy contribution to the total energy of quasi-two-dimensional hole systems realized by a hard-wall quantum-well confinement of valence-band states in typical semiconductors. The magnitude of the exchange energy turns out to be suppressed from the value expected for analogous conduction-band systems whenever the mixing between heavy-hole and light-hole components is strong. Our results are obtained using a very general formalism for calculating the exchange energy of many-particle systems where single-particle states are spinors. We have applied this formalism to obtain analytical results for spin-3/2 hole systems in limiting cases.